Please use Python
Write a program that finds the average of a series of numbers entered by the user. As in the previous problem, the program will first ask the user how many numbers there are. Note: the average should always be a float, even if the user inputs are all ints. Write a program that approximates the value of T by summing the terms of this series: 4/1 4/3 +4/5 - 4/7 +4/9- 4/11 +... The program should prompt the user for n, the number of terms to sum, and then output the sum of the first n terms of this series. Have your program subtract the approximation from the value of math.pi to see how accurate it is A Fibonacci sequence is a sequence of numbers where each successive number is the sum of the previous two. The classic Fibonacci sequence begins: 1, 1, 2, 3, 5, 8, 13,.... Write a program that computes the nth Fibonacci number where n is a value input by the user. For example, if n - 6, then the result is 8. You have seen that the math library contains a function that computes the square root of numbers. In this exercise, you are to write your own algorithm for computing square roots. One way to solve this problem is to use a guess-and-check approach. You first guess what the square root might be and then see how close your guess is. You can use this information to make another guess and continue guessing until you have found the square root (or a close approximation to it). One particularly good way of making guesses is to use Newton's method. Suppose x is the number we want the root of and guess is the current guessed answer. The guess can be improved by usias the next guess. Write a program that implements Newton's method. The program should prompt the user for the value to find the square root of (x) and the number of times to improve the guess. Starting with a guess value of x/2, your program should loop the specified number of times applying Newton's method and report the final value of guess. You should also subtract your estimate from the value of math.sqrt (x) to show how close it is. quess+ Write a program that finds the average of a series of numbers entered by the user. As in the previous problem, the program will first ask the user how many numbers there are. Note: the average should always be a float, even if the user inputs are all ints. Write a program that approximates the value of T by summing the terms of this series: 4/1 4/3 +4/5 - 4/7 +4/9- 4/11 +... The program should prompt the user for n, the number of terms to sum, and then output the sum of the first n terms of this series. Have your program subtract the approximation from the value of math.pi to see how accurate it is A Fibonacci sequence is a sequence of numbers where each successive number is the sum of the previous two. The classic Fibonacci sequence begins: 1, 1, 2, 3, 5, 8, 13,.... Write a program that computes the nth Fibonacci number where n is a value input by the user. For example, if n - 6, then the result is 8. You have seen that the math library contains a function that computes the square root of numbers. In this exercise, you are to write your own algorithm for computing square roots. One way to solve this problem is to use a guess-and-check approach. You first guess what the square root might be and then see how close your guess is. You can use this information to make another guess and continue guessing until you have found the square root (or a close approximation to it). One particularly good way of making guesses is to use Newton's method. Suppose x is the number we want the root of and guess is the current guessed answer. The guess can be improved by usias the next guess. Write a program that implements Newton's method. The program should prompt the user for the value to find the square root of (x) and the number of times to improve the guess. Starting with a guess value of x/2, your program should loop the specified number of times applying Newton's method and report the final value of guess. You should also subtract your estimate from the value of math.sqrt (x) to show how close it is. quess+
